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# Course Modules for First Year B.A. Mathematics

## OBJECTIVES:

Number theory is a foundational branch of mathematics. This module gives the student a solid grounding in the subject.

## LEARNING OUTCOMES:

Students who successfully complete this module should be able to:

• understand the basic elements of number theory;
• understand notation and conventions associated with the topic;
• use known algorithms to solve problems related to divisibility;
• master modular arithmetic;
• produce coherent and convincing arguments;
• communicate solutions to problems clearly and coherently.

## MODULE CONTENT:

• Representations of numbers;
• The binomial theorem; Mathematical induction;
• Divisibility of integers; Prime Numbers and The Fundamental Theorem of Arithmetic;
• Euclid's algorithm
• Congruence; linear Diophantine equations; Fermat's Little Theorem; Using congruences to solve more complex problems;
• Pythagorean Triples.

## PRIME TEXTS:

ORE, O. (1969). Invitation to Number Theory. Mathematical Association of America.

SILVERMAN , J. H. (2012). A Friendly Introduction to Number Theory. Pearson Education.

## OTHER RELEVANT TEXTS:

NIVEN, I.M., ZUCKERMAN, H.S. (1980). An introduction to the theory of numbers, Wiley.

DUDLEY, U. (2008). Elementary Number Theory, Dover.

BURN, R.P. (1997). A pathway into number theory, Cambridge University Press.

FORMAN, S., RASH, A. (2015). The Whole Truth About Whole Numbers, Springer.

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## OBJECTIVES:

Geometry is a core part of mathematical education, because it provides a paradigm of rigorous mathematical reasoning. This module equips students with basic knowledge and skills of euclidean geometry. It thereby prepares the student for the study of other areas of mathematics.

## LEARNING OUTCOMES:

Students who successfully complete this module should be able to:

• understand, express and use geometric results;
• carry out geometric constructions;
• determine certain geometric quantities from others;
• use coordinates to solve geometric problems analytically.

## MODULE CONTENT:

• angle, distance, length, area;
• coordinates;
• lines, triangles and circles;
• geometric constructions;
• congruence and similarity.

## PRIME TEXTS:

OSTERMANN, A., WANNER, G. (2012). Geometry by Its History, Springer.

LANG, S., MURROW, G. (1988). Geometry, Springer.

GARDINER, A. D., BRADLEY, C. J. (2005). Plane Euclidean Geometry: Theory and Problems, The United Kingdom Mathematics Trust.

## OTHER RELEVANT TEXTS:

BRUMFIELD, C. F., VANCE, I. E. (1970). Algebra and Geometry for Teachers, Addison-Wesley.

CLARK, D. M. (2012). Euclidean Geometry: A Guided Inquiry Approach, American Mathematical Society.

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